At the same time, we call the number of points of the largest complete graph subgraph included in Figure F as “clique number“, and note it as X. It is easy to find that a complete graph of n points requires at least n different colors because the two points are adjacent.
.........
It is obvious from the above that any part of a graph is divided and dyed to make any part with common sidelines have different colors, and can only use four colors, no more. The proposition is true.